Your title gets you into the meeting. How you treat the quiet person in it gets you the team.

Whatever room you are in, people learn who you are from how you treat whoever has the least standing in it. The person saying nothing is the easiest to overlook, which makes them the clearest test. Everyone else is watching that and deciding whether you are safe to be honest around. A seat at the table is handed to you; loyalty gets earned at the edges of it.

In your next meeting, ask the quietest person a direct question and leave room for the answer. Credit them by name if their idea gets used. Do it whether or not anyone senior is watching.